I am reading something about electomagnetic field and the first introduce the free space permittivity and permeability for the electric field and magnetic field. And later when discussing the field in the material, the introducing the permittivity and permeability as the multiplication of the relative quantity and the free space one, i.e. $\varepsilon = \varepsilon_r\varepsilon_0$ and $\mu=\mu_r\mu_0$. For vacuum, we have $\varepsilon_r=1, \mu_r=1$. From the physical point of view, why we have to do this way and why we have to define the relative permittivity and relative permeability instead of just giving the actual permittivity and permeability for the material? Also, what that 'relative' refer to?

1 Answer
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Well, the relative quantities crop up more than the absolute ones at times. For example, the susceptibilities are defined as $\chi_e + 1 =\epsilon_r, \chi_v+1=\mu_r$. They come up in equations like $ \mathbf M=\chi_v\mathbf H$.

Aside from this, in most cases, writing in terms of $\epsilon_r$ lets $\epsilon_0$ "float to the top" of equations, which makes them more elegant ($\epsilon_0+2\epsilon$ vs $\epsilon_0(1+2\epsilon_r)$). This echoes Cheeku's comment above "$x = 4.02569453$ and $y = 0.12x$ is actually better than saying $x = 4.0256945$ and $y = 0.4830833436$."

Finally, using the relative values means that you need not convert data from one system of units to another.

Still, there are some cases where the absolute constants are better. In my experience, the two are used interchangeably, though most writers prefer the relative constants for the reasons given above.